Separating the Yes- from the No-Instances in the Number Partitioning Problem
Ruben Horn, Reitze Jansen, Okke van Eck, Daan van den Berg · 2024
The (two-way) number partitioning problem (NPP) is a well known NP-complete decision problem in which a set of (positive) integers must be split in such a way that the sum of both resulting subsets is equal. However, its optimization problem variant is even harder, since the verification of partitions is only possible in polynomial time for instances which have a perfect partition. We investigate the distribution of instances that have and that do not have a perfect partition, and find that they are not randomly distributed in the instance space. Thus, the hardness of any given instance might be predictable to some extent. We demonstrate that it is possible to separate these two instance types visually using a linear time embedding into R 2 for instances of the same template. Furthermore, we compare three greedy heuristic algorithms (greedy captains, greedy coach, and greedy tyrant) and their difference to the solution from an exact branch-and-bound (BB) algorithm.